I am so proud of you for reaching out for some support, some comfort and some conversation around what I can hear is tearing you up inside. You know you are not a bad person and that you have made a mistake, we all do it, and yes, if it was so easy to accept and to stand up and move on well there would be half as many people suffering today. However this does not get to win, to consume you, to dictate the rest of your life and hold you prisoner, to live in the dark and to see no hope.
You mention a really great point, it isn't you, it should not define who you are and it doesn't, and sometimes the fact that others have forgiven makes it even harder...the noise in your head that "how can you forgive me when I can not even forgive me?". This is not who you are, you made a mistake, but it does not define you.
I agree with the statement that nothing, and I really do mean nothing is ever a mistake if you have learnt from it, I can hear you are truly remorseful for what you did, that you do want to move on, so I can assume from that that you did LEARN from that incident, that the lesson was learnt. I hear you say "well I don't need to kill someone to know it is wrong"...indeed....however, mostly we know this lesson to be true and don't need to fill it to have learnt.
Forgiveness is very hard, and self forgiveness even more so. How would you feel about writing a letter to yourself, apologizing for what you have done, not for the act but the way you are now treating yourself. That you have been forgiven by other parties and now it is time to accept the apology for you.
Sitting with the guilt and shame is also another tool, you can acknowledge that these feelings are coming, allow yourself to feel like that and put a time on it, sit with it for 1 minute or 2 minutes then allow yourself to move forward, by doing something nice for you, something you enjoy and something that does give you joy.
I think another part of the process is acknowledging why you did this mistake and taking measures to ensure you don't ever repeat it. There is safety in knowledge and power to gain from knowing you will not be doing this again. This might be really hard to admit the root cause as to why, but perhaps some raw and honest writing can help you with this, you don't even have to show anyone.
I wish you peace and progress Anzacspirit, it is time now for you to breathe and to receive love, and to be allowed to.